Technical Comments

Time-Variable Cratering Rates?

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Science  23 Jun 2000:
Vol. 288, Issue 5474, pp. 2095
DOI: 10.1126/science.288.5474.2095a

Using stepwise laser-heating methods, Culler et al. (1) determined the40Ar/39Ar formation ages of 155 lunar impact melt beads from a soil sampled during the Apollo 14 mission. Because relatively old ages of >3 billion years (Gy) and fairly young ages of <0.4 Gy dominate, Culler et al. concluded that the cratering rate in the inner solar system decreased by a factor of 2 to 3 during the past 3 Gy and then intensified again during the most recent 0.4 Gy.

Petrographic analysis of lunar soils reveals irregular, dark-colored melt particles, termed agglutinates, that compositionally resemble the fine soil fraction (2), and regularly shaped melt beads that are distinctly colored and have bulk compositions akin to those of local surface rocks (3). Small-scale impacts into powdered soil apparently produce agglutinates, and similar impacts into competent rock produce melt beads (4). The particles analyzed by Culler et al. seem to be of the bead type.

The agglutinate content may reach 50% by volume in any lunar soil, whereas beads rarely exceed 5%, a distribution grossly consistent with the fractional surface areas occupied by fine-grained soil and rocks on the present-day moon. This soil-to-rock ratio evolves systematically with time, however. Any terrain rejuvenated by volcanism or impacts will initially consist of rock, from which even the smallest impact can produce only melt beads. Conceptually, the production of such beads will be controlled by the fractional surface area occupied by rock—initially as genuine bedrock, in later stages as freshly excavated boulders. With increasing regolith thickness the system becomes progressively self-buffering, and larger and larger craters are required to emplace fresh bedrock boulders at the surface (5). These processes cause the production rate of surface rocks to decrease progressively with time, with a corresponding decrease in the production rate of melt beads.

This average scenario includes the occasional impact that penetrates deeply into bedrock and produces a substantial boulder field at the surface. Such local stochastic anomalies can lead to distinct spikes in the age distribution of melt beads and could cause the seeming increase in cratering activity at 0.4 billion years ago (Ga) reported by Culleret al. The supposed increase may also relate to bead preservation: any ideal production function for melt beads will be modulated by some destruction function. Recently produced beads may be overrepresented in this population because they have experienced a relatively benign bombardment history compared with that of the average soil.

For a constant cratering flux, the self-buffering effects of the evolving debris layer would cause the absolute growth rate of regolith to decrease by a factor of 3 to 4 over the past 3 Gy (5). The production of melt beads may vary by similar factors. Thus, the distribution of bead ages reported by Culler et al. might be consistent with a constant impactor flux. In addition, lunar soils are the products of stochastic processes, and individual samples could have highly idiosyncratic histories; any one soil sample might not faithfully represent the average cratering history through geologic time. Obviously, additional soils need to be investigated using the methods pioneered by Culler et al.


Response: Hörz draws attention to the fact that spherule age measurements at a single location can be affected by the peculiar local cratering history, and that our reported variations in spherule numbers with age may not directly reflect the moon's global bombardment history. We agree; local effects can indeed distort the local record, so measurements at multiple locations are necessary before a definitive cratering rate can be established.

One should not incorrectly deduce from Hörz's comment, however, that the assumption of constant cratering rate for the last 3 Gy is firmly grounded in data. It is instead based on indirect evidence of the ages of craters Tycho, Copernicus, Aristillus, and Autolycus. The age of Tycho, for example, is based on cosmic-ray exposure ages of materials from the Apollo 17 mission that were dislodged in a debris slide assumed to have been triggered by secondary Tycho impacts. The cratering rates from these previous estimates are imprecise enough to be consistent with either a constant cratering rate or the variable rate we reported [figure 3 of (1)].

If we purposely ignore the precision of our spherule ages and group the events into bins of 1-Gy duration, the production rate appears to be constant over the past 3 Gy (solid line in Fig. 1). Grouping the spherule ages into 0.4-Gy bins (which is justified by our 0.15-Gy median age uncertainty), by contrast, shows the reported decrease from 3 Ga to 0.4 Ga, followed by a sudden increase during the past 0.4 Gy. Had our age resolution been less accurate and the larger bins been used, we might have concluded that the impact rate was approximately constant.

Figure 1

Histogram of spherule ages. The dotted line shows the histogram with the 0.4-Gy bin width, as used in Culler et al. (1). The solid line shows the same data with 1-Gy bins. Larger numbers show the total number of events in each 1-Gy bin; smaller numbers show total number of events in each 0.4-Gy bin. With 1-Gy bins simulating a degradation of age uncertainty, the data are consistent with a constant impact rate over the past 3 Gy.

Some may argue that constant cratering is the simplest hypothesis consistent with the data and thus better satisfies Occam's razor. We disagree. Previous measurements on the moon, the Earth, and in astronomical observations had suggested an increase in recent cratering (2–6), although not as large as the one we deduced. To make our data consistent with a constant impact rate, Hörz assumes that the spherule production comes primarily from impacts on rocks, not regolith. That is only a hypothesis (7), however: although it is suggested by chemical analysis, critical laboratory tests have never been performed. If this hypothesis is correct, then a gradual decrease in spherule production would be expected as the rock component of the regolith is gradually comminuted. To explain the sudden increase observed at 0.4 Gy, one must also hypothesize a sudden increase of rock component caused by a local large impact at that time. Spherule measurements at another lunar site presumably would not be sensitive to a local impact at 0.4 Ga, and thus could provide a test of Hörz's model. Such measurements are under way.

Of course, the unverified nature of Hörz's model does not make it wrong, or even implausible. It is an alternative interpretation of our data that deserves testing. Nevertheless, in our judgment, reconciling a constant cratering rate with our spherule data requires enough additional assumptions that the constant-rate hypothesis no longer qualifies as Occam's favorite.


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